* Just who is this Ice King??
You could get arguments forever on that. It may literally be the 13th Commander of the Night's Watch, who would be thousands of years old. But it also may be someone of whom we've never heard.
Did the Kingslayer really slay the Mad King??
Yes, absolutely.
Did they burn Aerys Targaryen after he was killed??
I don't believe so.
** Speaking of the icy dead....do you suppose Caitlyn Stark is out there someplace still?? After the Red Wedding they tossed her dead body into the river and it was never seen again...
In the books, she is still out there as a revived, intelligent undead, last seen as sort of the spiritual head of the Brotherhood without Banners. That whole storyline was supposedly scotched from the show, but there's nothing saying they couldn't revive it given that Sandor seems to be headed that way. And since he's the last one in Westeros who had any contact with Arya, I suppose it might be possible that UnCatelyn could command him to go find/rescue her.
*** Who ever thought that the Hound could be a hero??
Well, way back in I think 1999, I posted a thread on an old ASOIAF message board about that very issue. It came about because there were some folks who just had their hearts set in Sansa eventually hooking up with the Hound, and I thought the Hound was an utter scumbag. But, I started a thread about what it would take for him to find redemption. And since then, I know there has been a general consensus in the fan community that Sandor eventually would find some form of redemption. Until maybe 3-4 years ago, you could still find shreds of that old board around, though it went inactive in about 2000 or so when it shifted over to another board, and then kept changing until it morphed into the Westeros board.
By the way, never ever go to that Westeros board and try to discuss politics. It makes DU look like Reagan.
**** Do you think The Mountain That Rides will survive another season??
Nope, he's a damn goner by the end of this season, but I think he's going to take a lot of people with him.
***** Interesting that episode six showed the Mad King ordering "burn them all!" with the liquid dragon fire. The first season underplayed the importance of dragon fire and just where it all came from. Supposedly by the time of the Mad King, all the dragons had died out, but those three eggs came from someplace and Aerys had gallons of the stuff. If you look at the scene of the dragon roaring you can see the two tubes, one on each side of the mouth, that the dragon excretes the liquid dragon fire from....
Well, if I understand you right, there are actually two different things going on in your post. The first is that the fire to which Aerys was referring is the same stuff Tyrion used in the battle of the Blackwater against Stannis' fleet, and it is actually a chemical called "wildfire" produced by pyromancer chemists at King's Landing. Aerys probably calls it "dragonfire" just out of vanity, but it wasn't really from dragons.